Sei sulla pagina 1di 41

Profit and Profitability

The word profitability is used as the general term for the measure
of the amount of profit that can be obtained from a given
Before capital is invested in a project or enterprise, it is necessary
to know how much profit can be obtained and whether or not it
might be more advantageous to invest the capital in another form
of enterprise.
Thus, the determination and analysis of profits obtainable from
the investment of capital and the choice of the best investment
among various alternatives are major goals of an economic
Profitability, therefore, is the common denominator for all
business activities
Profitability Standards
The profits anticipated from the investment of funds
should be considered in terms of a minimum
profitability standard.
A profitability standard is a quantitative measure of
profit with respect to the investment required to
generate that profit.
This profitability standard, which can normally be
expressed on a direct numerical basis, must be weighed
against the overall judgment evaluation for the project
in making the final decision as to whether or not the
project should be undertaken.
Thus, it must be recognized that the profit
evaluation is based on a prediction of future results
so that assumptions are necessarily included.
Many intangible factors, such as future changes in
demand or prices, possibility of operational failure,
or premature obsolescence, cannot be quantitized.
It is in areas of this type that judgment becomes
critical in making a final investment decision.
An obvious set of alternatives involves either making
the capital investment in a project or investing the
capital in a safe venture for which there is essentially
no risk and a guaranteed return.
Cost of Capital
Cost of capital is the amount paid for the use
of capital from such sources as bonds,
common and preferred stocks and loans.
The argument for using the cost of capital as a
basic profitability standard is that any project
must earn at least that rate to repay these
external capital sources.
Hence the simplest approach is to assume
that investment of capital is made at rate of
return equivalent to the total profit or rate of
return over the full expected life of the
particular project.
This method has the advantage of putting the
profitability analysis of all alternative
investments on an equal basis, thereby
permitting a clear comparison of risk factors.
Mathematical Methods of Profitability
1. Rate of return on investment
2. Discounted cash flow based on full-life
3. Net present worth
4. Capitalized costs
5. Payout period
Rate of Return on Investment
In engineering economic studies, rate of return
on investment is ordinarily expressed on an
annual percentage basis.
The yearly profit divided by the total initial
investment necessary represents the fractional
return, and this fraction times 100 is the
standard percent return on investment.
Profit is defined as the difference between
income and expense.
Therefore, profit is a function of the quantity of
goods or services produced and the selling
The amount of profit is also affected by the
economic efficiency of the operation, and
increased profits can be obtained by use of
effective methods which reduce operating
To determine the profit, estimates must be made of
direct production costs, fixed charges including
depreciation, plant overhead costs, and general
Profits may be expressed on a before-tax or after-tax
basis, but the conditions should be indicated. Both
working capital and fixed capital should be considered
in determining the total investment.
If the return is zero or larger, the investment will be
attractive. This method is sometimes designated as
return bused on capital recovery with minimum profit.
Return on investment
(Rate of return)
A simple measure of economic performance.

ROI=[(net annual profit)/(total investment)]*100

Net profit is usually not constant from year to year for a

project also additional investment may be made during
the project life so we cannot take a particular year for
calculation of ROI. So we take average ROI over the
entire project life.
If ROI is calculated as an average over the
whole project then

ROI=[(cumulative net profit)/(plant life*initial


It is possible that investments made later on

after the original investment may be very
small compared to the original investment so
we can ignore them and include average profit
per year.
Minimum Acceptable Rate of
It is the earning that must be achieved by an
investment in order for it to be acceptable to
the investor.
It is used as a fraction per year but often
expressed as percentage per year.
The Mar on generally is based on the highest
rate of earning on safe investment that is
available to the investor such as corporate bond
government bonds and loans.
Table: Suggested values for risk and minimum acceptable return on investments

Investment Type Level of Risk Minimum Acceptable Rate of

Return(Mar)(after income

Basis: Safe Corporate investment Safe 4-8

opportunities or cost of capital

New Capacity with established Low 8-16

corporate market position

New product entering into Medium 16-24

established market or new process

New product or process in a new High 24-32


Everything new, high R& D and Very High 32-48+

marketing effort
Methods For Calculating Profitability
Methods that do not Consider Time Value of
1) Rate of Return on Investment
2) Payback Period
3) Net Return
Pay-back time
A simple method for estimating pay back time is
to divide total initial capital (fixed plus working
capital ) by the average annual cash flow.
The payout period is the length of time
necessary for the total return to equal the
capital investment. The initial fixed capital
investment and annual cash flow are usually
used in this calculation
Simple pay back time = (total investment)/(average
annual cash flow)
The payout period is the length of time necessary for
the total return to equal the capital investment. The
initial fixed capital investment and annual cash flow
are usually used in this calculation so the equation is

Where PBP is payback period in years V the

manufacturing fixed capital investment, Ax the
nonmanufacturing fixed capital investment and Aj
the annual cash flow
But cash flow usually changes from year to
year so we have to include cash flow for each
year or average cash flow (Aj)ave in the
equation for PBP
Net Return
It is the amount of cash flow over and above that
required to meet the minimum acceptable rate of
return and recover the total capital investment.

This quantity is calculated by subtracting the total

amount capital investment, from the total cash flow.

Each of these quantities represents the total amount

obtained over the length of the evaluation period
The net return is given by:

Where Rn is the net return in dollars and recj the dollars

recovered from the working capital and the sale of physical
assets (equipment, buildings, lands etc.) in year j.
The sum of dj plus the sum of the recovered amounts is equal
to total capital investment or the sum of Tj, the equation
simplifies to
and when divided by N, the equation becomes

where Rn,ave is the average net return in

dollars per year
Any positive value for Rn indicates that the
cash flow to the project is actually greater
than the amount necessary to repay the
investment and obtain a return that meets the
minimum acceptable rate. Therefore, it is
earning at a rate greater than minimum
acceptable rate.
If Rn happens to equal zero, then the project is
repaying the investment and matching the
required mar
Methods that Take Time Value of
Money into Account
Net present worth (NPW):
The net present worth is the total of the
present worth of all cash flow minus the
present worth of all capital investment, as
defined by

sum of all present worth of cash flow is

CFn=cash flow in year n

NPW is the net present worth,
PWFcfj is the selected present worth factor for
the cash flow in year j,
sj the value of sales in year j,
coj the total product cost not including
depreciation in year j,
PWFv,j the appropriate present worth factor for
investment occurring in year j,
Tj is the total investment in year j.
An earning rate is incorporated into the
present worth factor by the discount rate
Thus, the net present worth is the amount of
money earned over and above the repayment
of all the investment and the earning on the
investment at the discount rate used in the
present worth factor calculations.
The appropriate discount rate to use for
discrete compounding is the minimum
acceptable rate of return or mar originally
selected as the evaluation standard. For
continuous compounding the nominal interest
rate is used, as given by

Where rma is the minimum acceptable

nominal rate for continuous compounding.
The net present worth is the time value of
money equivalent of the net return.
If the net present worth positive, then the
project provides a return at a rate greater than
the discount rate used in the calculation.
In making comparisons of investment, the
larger the net present worth, the more
favourable is the investment
If the net present worth is equal to zero, then
the project provides a return that matches the
discount rate.
In either of these cases, the project is judged
as favourable compared to mar selected.
If the net present worth is less than zero, then
the project rates unfavourably with respect to
the mar standard.
The net present value is always less than the
total future worth of the project because of the
discounting of future cash flows.
The net present value is strong function of
interest rate and the time period studied.
Net present value is more useful economic
measure than the simple pay back and rate on
investment, since it allows for the time value of
money and also for annual variation in expenses
and revenues.
Time value of money
In cash flow diagram, the net cash flow is shown
at is value in the year in which it occurred .
So the number on the coordinate show the
future worth of he project. The cumulative value
is the net future worth(NFW).
The money earned in any year can be reinvested
as soon as it is available and can start to earn
return. So money earned in the early years of
the project is more valuable than the earned in
later years.
This time value of money can be allowed for by using
a variation of familiar compound interest formula.
The net cash flow in each year of the project is
brought to its present value at the start of the
project by discounting it at some chosen compound
The future worth of amount of money , P, invested at
interest rate i for n years is
Future worth in n years=P(1+i)^n
Hence present value of the sum is,
present value of the future sum=
(future worth in year n)/[(1+i)^n]
The interest rate used in the discounting
future values is called the discounting rate.
Discounting of the future cash flows should
not be confused with allowing for price
Inflation is a general increase in prices and
costs, usually caused by imbalance between
supply and demand.
Discounting on the other hand is a means o f
comparing the value of money that is available
now (and can be reinvested) with money that
will become available at some time in the
Rate of Return Based on Discount
Cash Flow
The method of approach for a profitability evaluation
by discounted cash flow takes into account the time
value of money and is based on the amount of the
investment that is unreturned at the end of each year
during the estimated life of the project.
The procedure has involved the determination of an
index or interest rate which discounts the annual cash
flows to a zero present value when properly compared
to the initial investment.
A trial-and-error procedure is used to establish a rate of
return which can be applied to yearly cash flow so that
the original investment is reduced to zero (or to salvage
and land value plus working-capital investment) during
the project life.
By calculating the net present value at various rates, it
is possible to find an interest rate at which the
cumulative net present value at the end of the project
is zero.
This particular rate is called the discounted cash flow
rate of return and is a measure of the maximum
interest rate that the project could pay and still break
even by the end of the project life.

Sum of present worth of cash flow is

The value of i is found by trial and error
A more profitable project will be able to pay a
higher discounted cash flow rate of return.
Thus, the rate of return by this method is equivalent to
the maximum interest rate (normally, after taxes) at
which money could be borrowed to finance the project
under conditions where the net cash flow to the project
over its life would be just sufficient to pay all principal
and interest accumulated on the outstanding principal.
Designate the discounted-cash-flow rate of return as i.
This rate of return represents the after-tax interest rate
at which the investment is repaid by proceeds from the
It is also the maximum after-tax interest rate at which
funds could be borrowed for the investment and just
break even at the end of the service life.
The discount factor for end-of year payments and annual
compounding is

D=1/[(1+i)^n]=discount factor
Where, i = rate of return
n = year of project life to which cash flow applies
This discount factor, d is the amount that would yield one
dollar after n years if invested at an interest rate of i.
The discounted-cash-flow rate of return can be
determined by the trial-and-error method where where
the annual cash flows are discounted by the appropriate
discount factor to a total present value equal to the
necessary initial investment
The capitalized-cost profitability concept is
useful for comparing alternatives which exist
as possible investment choices within a single
overall project.
For example, if a decision based on
profitability analysis were to be made as to
whether stainless steel or mild steel should be
used in a chemical reactor as one part of a
chemical plant, capitalized-cost comparison
would be a useful and appropriate approach.
Capitalized cost related to investment
represents the amount of money that must be
available initially to purchase the equipment
and simultaneously provide sufficient funds for
interest accumulation to permit perpetual
replacement of the equipment.
If only one portion of an overall process to
accomplish a set objective is involved and
operating costs do not vary, then the
alternative giving the least capitalized cost
would be the desirable economic choice.
The basic equation for capitalized cost for
equipment is,

K = capitalized cost
C, = original cost of equipment
C, = replacement cost
V, = salvage value at end of estimated useful life
n = estimated useful life of equipment
i = interest rate
Where is capitalized cost factor
Example 5